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3 years ago

Which step should be used to prove that point P is equidistant from R and Q?

Mathematics

1 answer:

mariarad [96]3 years ago

5 0

Equidistance means
Distance from R to P equals
Distance from Q to P.

So, in mathematical form,
PR = PQ

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After t years, the remaining mass y (in grams) of an initial mass of 35 grams of a radioactive element whose half- life is 80 ye

IgorC [24]

Answer: There will be 22.694 grams of initial mass remains after 50 years.

Step-by-step explanation:

Since we have given that

$y=35(\dfrac{1}{2})^{\frac{t}{80}$

We need to find the quantity of initial mass remains after 50 years.

So, t = 50 years,

We get that

$y=35(\dfrac{1}{2})^{\frac{50}{80}}\\\\y=35(0.5)^{0.625}\\\\y=22.694$

Hence, there will be 22.694 grams of initial mass remains after 50 years.

3 0

4 years ago

What is the standard form of an exponential function

dsp73

An exponential function is a function in which the independent variable is an exponent. Exponential functions have the general form y = f (x) = ax, where a > 0, a≠1, and x is any real number. The reason a > 0 is that if it is negative, the function is undefined for -1 < x < 1.

3 0

3 years ago

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 13001300

Ket [755]

Answer:

No, there is not enough evidence at the 0.02 level to support the strategist's claim.

Step-by-step explanation:

We are given that a political study took a sample of 1300 voters in the town and found that 57% of the residents favored construction.

And, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 54%, i.e;

Null Hypothesis, $H_0$ : p = 0.54 {means that the percentage of residents who favor construction is 54%}

Alternate Hypothesis, $H_1$ : p > 0.54 {means that the percentage of residents who favor construction is more than 54%}

The test statistics we will use here is;

T.S. = $\frac{\hat p -p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }$ ~ N(0,1)

where, p = actual percentage of residents who favor construction = 0.54

$\hat p$ = percentage of residents who favor construction in a sample of

1300 voters = 0.57

n = sample of voters = 1300

So, Test statistics = $\frac{0.57 -0.54}{\sqrt{\frac{0.57(1- 0.57)}{1300} } }$

= 2.185

Now, at 0.02 significance level, the z table gives critical value of -2.3263 to 2.3263. Since our test statistics lie in the range of critical values which means it doesn't lie in the rejection region, so we have insufficient evidence to reject null hypothesis.

Therefore, we conclude that the percentage of residents who favor construction is 54% and the strategist's claim is not supported.

4 0

4 years ago

Which explains whether the sum of 0.52 +0.61 is less than or greater than 1?

elixir [45]

Answer:

C. The sum is greater than 1 because the sum shades more than one hundredths grid.

Step-by-step explanation:

Given:

The sum of 0.52 + 0.61

= 0.52 + 0.61

= 1.13

The sum of 0.52 + 0.61 is greater than 1 with a value of 0.13

0.52 + 0.61 > 1

There are 10 tenth in 1 and 100 hundredth in 1

The sum of 0.52 + 0.61 will give 100 hundredth + 13 hundredth

The sum is greater than 1 because the sum shades more than one hundredths grid.

Picture of a hundredth grid is attached for better understanding

From the picture, 4 hundredth is shaded that is 0.04

4 0

3 years ago

Real numbers are ________ under addition. Integers are______ under division. Irrational numbers are _______ under multiplication

nata0808 [166]

<span>Real numbers are closee under addition.

Explanation: that means that the addtion of two real numbers is always a real number.

Integers are not closed under division.

Explanaton: that means that when you dived an integer number by another integer number the result may be a non integer number.

Irrational numbers are not closed under multiplication.

Explanation: that means that the multiplication of two irrational numbers may result in a rational number.

Rational numbers are closed under subtraction.

Explanation: that means that the result of the subtraction of rational numbers is always a rational number.
</span>

6 0

3 years ago